Vol. 36, No. 2, 1971

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Matrix rings of finite degree of nilpotency

Abraham A. Klein

Vol. 36 (1971), No. 2, 387–391

The degree of nilpotency of a ring R is defined to be the supremum of the orders of nilpotency of its nilpotent elements and it is denoted by ν(R). We consider the degree of nilpotency of the ring of m × m matrices Rm over a ring R. We obtain given results concerning the degrees ν(Rm) for distinct m’s, in the case R has no nonzero two-sided annihilators. It is shown that if )(Rm) = m for some m, and if Ris a ring containing R as an ideal such that Rhas no nonzero two-sided annihilators of R, then ν(Rm) = m. An application of this result is given.

Mathematical Subject Classification
Primary: 16.32
Received: 25 February 1970
Published: 1 February 1971
Abraham A. Klein